Two special classes of spacetimes admitting a non-null valence 2 Killing spinor

Non-conformally flat spacetimes admitting a non-null Killing spinor of valence 2 are investigated in the Geroch-Held-Penrose formalism. Contrary to popular belief these spacetimes are not all explicitly known. It is shown that the standard construction hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations, KS1 and KS2, for the spin coefficients and the components of the Ricci spinor. An exhaustive list of (conformal classes of) spacetimes, in which either KS1 or KS2 are violated, is presented. The resulting spacetimes are each other's Sachs transforms, in general admit no Killing vectors and are characterized by a single arbitrary function.

@article{839578,
abstract = {Non-conformally flat spacetimes admitting a non-null Killing spinor of valence 2 are investigated in the Geroch-Held-Penrose formalism. Contrary to popular belief these spacetimes are not all explicitly known. It is shown that the standard construction hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations, KS1 and KS2, for the spin coefficients and the components of the Ricci spinor. An exhaustive list of (conformal classes of) spacetimes, in which either KS1 or KS2 are violated, is presented. The resulting spacetimes are each other's Sachs transforms, in general admit no Killing vectors and are characterized by a single arbitrary function.},
author = {Van den Bergh, Norbert},
issn = {0264-9381},
journal = {CLASSICAL AND QUANTUM GRAVITY},
keyword = {TIMES,INVERTIBILITY,CONGRUENCES,FIELD-EQUATIONS,COSMOLOGICAL CONSTANT,ORTHOGONAL TRANSITIVITY,YANO TENSORS,NULL GEODESIC SEPARABILITY,general relativity,Killing spinors},
language = {eng},
number = {1},
title = {Two special classes of spacetimes admitting a non-null valence 2 Killing spinor},
url = {http://dx.doi.org/10.1088/0264-9381/27/1/015004},
volume = {27},
year = {2010},
}